There are actually one or two flights from CHC to AKL that operate between the international terminals, as they are the extension of an international flight. I'm assuming you must actually be on one of these if you're in C class, since there's no business class on regular NZ domestic flights.

Easy ways to tell if it's an 'international' flight between CHC and AKL are
(a) if the flight number has 2 digits not three
(b) if the a/c is a 747 or a 767-300
(c) if it has business class.a
Being on an international rather than domestic flight will make your transit at AKL much easier, and presumably you'll have to exit the country at CHC.